Externally definable sets and dependent pairs
Logic
2011-09-16 v2
Abstract
We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence.
Keywords
Cite
@article{arxiv.1007.4468,
title = {Externally definable sets and dependent pairs},
author = {Artem Chernikov and Pierre Simon},
journal= {arXiv preprint arXiv:1007.4468},
year = {2011}
}
Comments
17 pages, some typos and mistakes corrected, overall presentation improved, more details for the examples are given